Description
Book SynopsisWhat is so special about the number 30? How many colors are needed to color a map? Do the prime numbers go on forever? Are there more whole numbers than even numbers? These and other mathematical puzzles are explored in this delightful book by two eminent mathematicians. Requiring no more background than plane geometry and elementary algebra, this
Trade Review"A thoroughly enjoyable sampler of fascinating mathematical problems and their solutions."--Science "Each chapter is a gem of mathematical exposition... [The book] will not only stretch the imagination of the amateur, but it will also give pleasure to the sophisticated mathematician."--American Mathematical Monthly
Table of Contents*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Introduction, pg. 1*1. The Sequence of Prime Numbers, pg. 9*2. Traversing Nets of Curves, pg. 13*3. Some Maximum Problems, pg. 17*4. Incommensurable Segments and Irrational Numbers, pg. 22*5. A Minimum Property of the Pedal Triangle, pg. 27*6. A Second Proof of the Same Minimum Property, pg. 30*7. The Theory of Sets, pg. 34*8. Some Combinatorial Problems, pg. 43*9. On Waring's Problem, pg. 52*10. On Closed Self-Intersecting Curves, pg. 61*11. Is the Factorization of a Number into Prime Factors Unique?, pg. 66*12. The Four-Color Problem, pg. 73*13. The Regular Polyhedrons, pg. 82*14. Pythagorean Numbers and Fermat's Theorem, pg. 88*15. The Theorem of the Arithmetic and Geometric Means, pg. 95*16. The Spanning Circle of a Finite Set of Points, pg. 103*17. Approximating Irrational Numbers by Means of Rational Numbers, pg. 111*18. Producing Rectilinear Motion by Means of Linkages, pg. 119*19. Perfect Numbers, pg. 129*20. Euler's Proof of the Infinitude of the Prime Numbers, pg. 135*21. Fundamental Principles of Maximum Problems, pg. 139*22. The Figure of Greatest Area with a Given Perimeter, pg. 142*23. Periodic Decimal Fractions, pg. 147*24. A Characteristic Property of the Circle, pg. 160*25. Curves of Constant Breadth, pg. 163*26. The Indispensability of the Compass for the Constructions of Elementary Geometry, pg. 177*27. A Property of the Number 30, pg. 187*28. An Improved Inequality, pg. 192*Notes and Remarks, pg. 197
